Loop space, (2,0) theory, and solitonic strings

Abstract

We present an interacting action that lives in loop space, and we argue that this is a generalization of the theory for a free tensor multiplet. From this action we derive the Bogomolnyi equation corresponding to solitonic strings. Using the Hopf map, we find a correspondence between BPS strings and BPS monopoles in four-dimensional super Yang-Mills theory. This enable us to find explicit BPS saturated solitonic string solutions.

The 3-Lie algebra (2,0) tensor multiplet and equations of motion on loop space

“…20) where we used D(Cẋ λ , ∇ λ H µνκ ) = 0 andẋ [ρẋσ] = 0. Equation(3.20) is simply the Bianchi identity for the field strengthF .…”

Closed non-Abelian strings

“…The on-shell supersymmetry variations for the components fields were obtained in [4]. It would be nice to see how to express this in terms of a superfield in a super loop space.…”

“…I am grateful to Urs Schreiber for having pointed this out to me. Another derivation can be found in[2,3,4].…”

M-theory branes and their interactions

“…H * is a more general form of G 5 , chosen to have the analogous properties {H * , X i } = 0 and (H * ) 2 = 1. In fact using these properties (130) reduces to the simpler form…”

“…The appearance of the deformation of the loop space by the presence of the background C field on the brane indicated that this may well be a way to view the five-brane. Ideas of this sort have been explored in [130,131] though as yet there is no clear theory of the five-brane. This article on M-theory is missing a key section on the Matrix models of M-theory [17].…”